In the field of evolution strategy, basic principles of natural evolution are used for generating or optimizing technical structures. Basic operations are mutation and recombination as a method for modifying structures or parameters. To eliminate unfavorable modifications and to proceed with modifications which increase the overall quality of the system, a selection operation is used. Principles of the evolution strategy can be found for example in Rechenberg, Ingo (1994) “Evolutions strategie”, Friedrich Frommann Holzboog Verlag.
With reference to FIG. 1 at first the known cycle of an evolution strategy will be explained.
In a step 1 the object parameters to be optimized are encoded as real numbers in a vector called individual or chromosome. One individual can alternatively also consist of several vectors or chromosomes. A number of such individuals are generated that comprise the initial parent generation and the quality (fitness) of each individual in the parent generation is evaluated. In a step S2 the parents are reproduced by applying operators called mutation and recombination. Thus, a new generation is produced in step S3, which is called the offspring generation. The quality of the offspring individuals is evaluated using a fitness function which is the objective of the optimization in step S4. Finally, depending on the calculated quality value, step S5 selects (possibly stochastically) the best offspring individuals (survival of the fittest) which are used as parents for the next generation cycle if the termination condition in step S6 is not satisfied.
In particular for this application the real number vector, the object parameter, represents the coding for a spline which describes a two or higher dimensional body. This mapping from the parameter vector to the spline encoded structure is usually referred to as the genotype (=the parameter vector)−phenotype (=the two or higher dimensional body) mapping. In order to determine the fitness in step S4, first the genotype is mapped to the phenotype and then the quality of the phenotype is derived. A particular example is the parameterization of an airfoil (=the phenotype) by a real-valued vector (=genotype) describing a spline which determines the geometry of the airfoil. Finally, the quality of the airfoil can be determined, e.g. by methods known from computational fluid dynamics.
The mutation operator for the reproduction in step S2 is realized by adding normal or Gaussian distributed random numbers to the already existing elements of the parameter set, the so-called chromosome. The step size of the mutation can be controlled by modifying the variance of the normal or Gaussian probability density function. The variances are called strategy parameters. In higher dimensions the strategy parameters can consist of all or some entries of the covariance matrix of the higher dimensional Gaussian probability density function. This method to control the mutation by means of strategy parameters particularly distinguishes evolution strategy from other evolutionary algorithms like genetic algorithms (GA) or genetic programming (GP).
Appropriate values for the strategy parameters are important for the convergence of the algorithm. The appropriate values depend on the problem and the actual position in the solution space. To adapt the mutation width online, different adaptation strategies are used. Some simple methods are the ⅕ rule (see Rechenberg) or the so-called mutative step size control. More complex methods are, for example, the de-randomized adaptation method or the co-variance matrix adaptation.
Evolution strategies have been shown to outperform other evolutionary algorithms like genetic algorithms or genetic programming for real-valued parameter optimization problems due to the above-mentioned possibilities of the adaptation or self-adaptation of the step size(s) of the mutation operator.